12/9 Bell Ringer (8th)

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the function. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

How do you find the equation of a line given two points?

Back

To find the equation of a line given two points (x1, y1) and (x2, y2), first calculate the slope (m) using m = (y2 - y1) / (x2 - x1). Then use the point-slope form y - y1 = m(x - x1) to find the equation.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) has exactly one output (y-value). A relation can have multiple outputs for a single input.

Front

What does it mean for a system of equations to be consistent?

Back

A system of equations is consistent if there is at least one solution that satisfies all equations in the system.

Front

What is the solution to a system of equations?

Back

The solution to a system of equations is the point (or points) where the graphs of the equations intersect.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How do you interpret the expression y = 3x + 2?

Back

In the expression y = 3x + 2, 3 is the slope, indicating that for every increase of 1 in x, y increases by 3. The y-intercept is 2, meaning the line crosses the y-axis at (0, 2).

Front

What is a vertical line and its equation?

Back

A vertical line is a line that goes straight up and down. Its equation is of the form x = a, where a is the x-coordinate of any point on the line.